Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada.
IEEE Trans Image Process. 2011 Aug;20(8):2211-20. doi: 10.1109/TIP.2011.2118217. Epub 2011 Feb 22.
Gradient estimators are mostly designed to yield accurate and robust estimates of the gradient magnitude, not the gradient direction. This paper proposes a method for the accurate and robust estimation of both the gradient magnitude and direction. It robustly estimates the gradient in the x- and y-directions. The robustness against noise is achieved by prefiltering and postfiltering of the gradient in each direction. To reduce edge blurring effects introduced by these filters, the gradient in a certain direction is obtained by applying the prefilter and postfilter in the perpendicular direction. The basic elements employed in each window are: highpass, lowpass and aggregation operators. The highpass operator is used as a gradient estimator, the lowpass operator is for prefiltering and postfiltering, and the aggregation operator is for aggregating the prefiltered and postfiltered gradients. Four different combinations of highpass, lowpass and aggregation operators are proposed: MVD-Median-Mean, MVD-Median-Max, RCMG-Median-Mean, and RCMG-Median-Max. Experimental results show that the RCMG-Median-Mean has the best performance in estimating the gradient and detecting the edges in noisy color images. It is computationally more efficient than the state-of-the-art gradient estimators and is able to accurately estimate the gradient direction as well as the gradient magnitude. Computer simulation results show that the proposed method outperforms other recently proposed color gradient estimators and edge detectors.
梯度估计器主要用于准确稳健地估计梯度幅度，而不是梯度方向。本文提出了一种准确稳健地估计梯度幅度和方向的方法。它在 x 和 y 方向上稳健地估计梯度。通过在每个方向上对梯度进行预滤波和后滤波，实现了对噪声的鲁棒性。为了减少这些滤波器引入的边缘模糊效应，在某个方向上获得梯度的方法是在垂直方向上应用预滤波器和后滤波器。每个窗口中使用的基本元素有：高通、低通和聚合运算符。高通运算符用作梯度估计器，低通运算符用于预滤波和后滤波，聚合运算符用于聚合预滤波和后滤波的梯度。提出了四种不同的高通、低通和聚合运算符的组合：MVD-中值-均值、MVD-中值-最大、RCMG-中值-均值和 RCMG-中值-最大。实验结果表明，RCMG-中值-均值在噪声彩色图像中的梯度估计和边缘检测方面表现最佳。它在计算上比最先进的梯度估计器更有效率，并且能够准确地估计梯度方向以及梯度幅度。计算机模拟结果表明，所提出的方法优于其他最近提出的彩色梯度估计器和边缘检测器。
